1-4 Assume that you are serving on the board of directors of a medium-sized corpora­tion, and you are responsible for establishing the compensation provided to senior management. You believe that the company's CEO is very talented, but your con­cern is that she may be looking for a better job and may want to boost the com­pany's short-run performance (perhaps at the expense of long-run profitability) to make herself look better to other corporations. What effect might these concerns have on the compensation policy you put in place?

1-5 If the overall stock market is extremely volatile, and if many analysts foresee the possibility of a stock market crash, how might that situation influence the way corporations choose to compensate their senior executives?

1-6 Teacher's Insurance and Annuity Association-College Retirement Equity Fund (TIAA-CREF) is the largest institutional shareholder in the United States, control­ling over $300 billion in pension funds. Traditionally, TIAA-CREF has acted as a passive investor. However, the organization recently announced a tough new cor­porate governance policy.

In a statement mailed to all 1,500 companies in which it invests, TIAA-CREF outlined a policy designed to improve corporate perform­ance, including a goal of higher stock prices for the stock assets it holds, and to encourage corp'orate boards to contain a majority of independent (outside) directors. TIAA-CREF wants to see management more account­able to shareholder interests, as evidenced by its statement that the fund will vote against any director "where companies don't have an effective, independent board which can challenge the CEO."

Historically, TIAA-CREF did not quickly sell poor-performing stock . In addition, the fund invested a large part of its assets to match the per­formance of the major market indexes, which effectively locked TIAA­CREF into ownership of companies in the indexes. Further complicating the problem, TIAA-CREF owns stakes of from 1 percent to 10 percent in several companies, and selling such large blocks of stock would depre their prices.

Common stock ownership confers a right to sponsor initiatives to shareholders regarding the corporation. A corresponding v ring right exists for shareholders.

a. Is TIAA-CREF an ordinary shareholder? b. Due to its asset size, TIAA-CREF must acquire large positions that it plans to

actively vote. However, who owns TIAA-CREF? c. Should the investment managers of a fund such as TIAA-CREF determine the

voting practices of the fund's shares, or should the voting rights be pa sed on to

TIAA-CREF's owners?

1-7 As a manager, do you care more about your company's market value, intrinsic value, or fundamental value? What about as an investor?

PR BlEMS

1-1 A Treasury bond that matures in 10 years has a yield of 6 percent. A lO-y ar cor­Default Risk Premium porate bond has a yield of 8 percent. Assume that the liquidity premium on the

corporate bond is 0.5 percent. What is the default risk premium on the corporate bond?

28 • Part 1 Fundamental Concepts

• •

, .:. Maturity Risk Premium

lliL lea! nsk.-!ree rate IS j percent, and intlation is expected to be 3 percent for the next 2 years. A 2-year Treasury security yields 6.2 percent. What is the maturity risk premium for the 2-year security?

CYBER BlEM Please go to the ThomsonNOW Web site to access any Cyberproblems.

ill ase Suppose you decided (like Michael Dell) to start a computer company. You know from experience that many students, who are now required to own and operate a personal computer, are having difficulty etting up their computers, accessing various m.ltcri­

als from the local college network and from the Internet, and installing new programs when they become available. Your immediate plan is to provide

a sen'ice unJer whi~h representatives of your com­pany will help students set up their computers, show them how to access various databases, and offer an e-mail "help desk" for various problems that will undoubtedly arise. You will also provide a gateway Web page to the campus computer center and the campus Intranet.

If things go well-and you think they will-you plan to purchase computers and offer them, with all required software fully installed, to students. More­over, you plan to develop your Web site with links to various destinations students will like, and as traffic to your site builds, to offer advertising services (and to charg for links) to local businesses. For example, omeone could go through your Web site to order

pizza while studying for a finance exam. Once you have established your company and

set up procedures for operating it, you plan to expand ro other colleges in the area, and eventually to go nationwide. At some point, probably sooner rather than later, you plan to go public with an IPO, then to buy a yacht and take off for the South Pacific. With these issues in mind, you need to answer f r yourself, and potential investors, the fol­lowing questions.

a.

b.

c.

d.

e.

f. g.

h.

I.

).

Why is corporate finance important to all managers? What ,should be the primary objectives of ma nagers? (1) Do firms have any responsibilities to society

at large? (2) Is stock price maximization good or bad for

society?

(3) Should firms behave ethically? What three aspects of cash flows affect the value of any investment? What are free cash flows? What are the three determinants of free cash flows? What is the weighted average cost of capital? What affects it? What are the components of the interest rate? How do free cash flows and the weighted aver­age cost of capital interact to determine a firm's value? When you first begin operations, assuming you are the only employee and only your money is invested in the business, would any agency prob­lems exist? Explain. If you expanded, and hired additional people to help you, might that give rise to agency problems? If you needed capital to buy an inventory of computers to sell to students, or to develop soft­ware to help run the business, might that lead to agency problems? Would it matter if the new capital came in the form of an unsecured bank loan, a bank loan secured by your inventory of computers, or from new stockholders (assuming you incorporate)?

Chapter 1 An Overview of Financial Management 29

• An adjustment to the formula must be made if the bond pays interest semi­annually: divide INT and rd by 2, and multiply N by 2.

• The return earned on a bond held to maturity is defined as the bond's yield to maturity (YTM). If the bond can be redeemed before maturity, it is call­able, and the return investors receive if it is called is defined as the yield to call (YTC). The YTC is found as the present value of the interest payments received while the bond is outstanding plus the present value of the call price (the par value plus a call premium).

• The longer the maturity of a bond, the more its price will change in response to a given change in interest rates; this is called interest rate risk. However, bonds with short maturities expose investors to high reinvestmetlt rate risk, which is the risk that income from a hond portfolio will decline because cash flows received from honds will be rolled over at lower interest rates.

• Corporate and l1lunicipal bonds have default risk. If an issller dd;'lults, inves­tors receive less than the promised return on the bond. Therefore, investors should evaluate a bond's default risk before making a purchase.

• There are many different types of bonds with different sets of features. These include convertible bonds, bonds with warrants, income bonds. purchasin power (indexed) bonds, mortgage bonds, debentures, subordinated debe ­tures, junk bonds, development bonds', and insured municipal bonds. Th return required on each type of bond is determined by the bond's riskiness.

• Bonds are assigned ratings that reflect the probability of their going into default. The highest rating is AAA, and they go down to D. The higher a bond's rating, the lower its risk and therefore its interest rate.

UESTIO S

4·1 Define each of the following terms: a. Bond; Treasury bond; corporate bond; municipal bond; foreign bond b. Par value; maturity date; coupon payment; coupon interest rate c. Floating-rate bond; zero coupon bond; original issue discount bond (OlD) d. Call provision; redeemable bond; sinking fund e. Convertible bond; warrant; income bond; indexed, or purchasing power, bond f. Premium bond; discount bond g. Current yield (on a bond); yield to maturity (YTM); yield to call (YTC) h. Reinvestment risk; interest rate risk; default risk i. Indentures; mortgage bond; debenture; subordinated debenture j. Development bond; municipal bond insurance; junk bond; investment-grade b nd

4·2 "The values of outstanding bonds change whenever the going rate of interest changes. In general, short-term interest rates are more volatile than long-term interest rates. Therefore, short-term bond prices are more sensitive to interest rate changes than are long-term bond prices." Is this statement true or false? Explain.

4-3 The rate of return you would get if you bought a bond and held it to its maturit} date is called the bond's yield to maturity. If interest rates in the economy ri after a bond has been issued, what will happen to the bond's price and to its YTM? Does the length of time to maturity affect the extent to which a given change in interest rates will affect the bond's price?

4-4 If you buy a callable bond and interest rates decline, will the value of your bond rise by as much as it would have risen if the bond had not been callable? Explain.

Chapter 4 Bond Valuation 145

4-5

ROBlEMS

41 Bond Valuation

4­Yield to Maturity;

Financial Calculator Needed

4-3 Yield to Maturity and Call;

Financial Calculator Needed

4·4 Current Yield

4·5 Bond Valuation

4·6 Bond Valuation

4·1 Yield to Maturity

A sinking fund can be set up in one of two ways: (1) The corporation makes annual paym' ts to the trustee, who invests the pro­

ceeds in securities (frequently governmeIlt bonds) and uses the accumulated total to retire the bond issue at maturit,.

(2) The trustee uses the annual payment· to retire a portion of the issue each year, either calling a given percentage of the issue by a lottery and paying a specified price per bond or buying bonds on the open market, whichever i, cheaper.

Discuss the advantages and disadvaIltages of each procedure from the viewpoint of both the firm and its bondholders.

Fine

Callaghan Motors' bonds have 10 year remallllllg to maturity. Interest is paid nnually, the bonds have a $1,000 par value, and the coupon interest rate is 8 per­

c nt. The bonds have a yield to maturity of <;I percent. What is the current market price of these bonds?

\'('ilson Wonders' bonds have l2 years n:maining to maturity. Interest is paid annually, the bonds have a $ I ,000 par value, and the coupon interest rate is 10 percent. The bonds sell at a price of $850. What is their yielJ to maturity?

Fina

Final

Tlatcher Corporation's bonds will mature in [0 years. The bonds have a faCt alue of $1,000 and an 8 perceIlt coupon rare, paid semiannually. The price of the

b nds is $1,100. The bonds are callable 111 5 years at a call price of $1,050. What j their yield to maturity? What is their yield to call?

Heath Foods' bonds have 7 years remainiutr to maturity. The bonds 11<1\'e a face value of $1,000 ~H1d a yield to m~1turity tlf 8 percent. They pay interest dl1l1Ualir

and have a 9 percent coupon rate. What is their curreIlt yield?

. 'ungesser Corporation has issued bon that have a 9 percent coupon we. payable semiannually. The bonds mature in 8 y' rs, have a face value of $1,000. and a yield to maturity of 8.5 pt:rceIlt. hat is the price of the bonds?

The Garraty Company has two bond . MIl'S outstanding. Both bonds pay $100 annual interest plus $l,OOO at maturity. B nd L has a maturity of 15 years, and Bond S a maturity of '1 year. a. What will be the value of each of these bonds when the going rate of interest i\

(1) 5 percent, (2) 8 percent, and (3) 12 percent? Assume that there is only one more interest payment to be made on B nd S.

b. Why does the longer-term (is-year) bond fluctuate more when interest rare\ change than does the shorter-term bond (1 year)?

The Heymann Company's bonds have 4 years remaining to maturity. Imerest i\ paid annually; the bonds have a $1,000 par value; and the coupon interest rate i,

percent. a. What is the yield to maturity at a current market price of (J) 5829 0;

(2) $\ ,104? b. Would you pay $829 for one of these bonds if you thought that the appropriar:

rate of interest was 12 percent-that 1 , If rd = 12%? Explain your answer.

146 Part 1 Fundamental Concepts

'\ .. Yield to Call

4-9 Bond Yields;

ial Calculator Needed

4·10 Yield to Maturity;

ial Calculator Needed

4·11 Current Yield;

. ICalculator Needed

4-12 ~ominallnterest Rate

4·13 Bond Valuation

4-14 est Rate Sensitivity; Financial Calculator

Needed

t.i .., ) LI'" db'"" 'I'll !jju kIvu CVJl.1IJcJJJ) ;)vlu d 20-) ell lJUlll1 l~ UC wHII a 1'+ per­

cent annual coupon rate and a 9 percent call premium. Today, Singleton called the bonds. The bonds originally were sold at their face value of $1,000. Compute the realized rate of return for investors who purchased the bonds when they were issued and who surrender them today in exchange for the call price.

A 10-year, 12 percent semiannual coupon bond with a par value of $1,000 may be called in 4 years at a call price of $1,060. The bond sells for $1,100. (Assume that the bond has just been issued.) a. What is the bond's yield to maturity? b. What is the bond's current yield? c. What is the bond's capital gain or loss yield? d. What is the bond's yield to call?

You just purchased a bond that matures in 5 years. The bond has a face value of $1,000 and has an 8 percent annual coupon. The bond has a current yield of 8.21 percent. What is the bond's yield to maturity?

A bond that matures in 7 years sells for $1,020. The bond has a face value of $1,000 and a yield to maturity of 10.5883 percent. The bond pays coupons semi­annually. What is the bond's current yield?

Lloyd Corporation's 14 percent coupon rate, semiannual payment, $1,000 par value bonds that mature in 30 years are ca'tlable 5 years from now at a price of $1,050. The bonds sell at a price of $1,.353.54, and the yield curve is flat. Assum­ing that interest rates in the economy are expected to remain at their current level, what is the best estimate of Lloyd's nominal interest ratc on new bonds?

Suppose Ford Motor Company sold an issue of bonds with a 10-year maturity, a $1,000 par value, a 10 percent coupon rate, and semiannual interest payments. a. Two years after the bonds were issued, the going rate of interest on bonds such

as th S' fcll to 6 percent. At what price would the bonds sell? b. Suppose that, 2 years after the initial offering, the going interest rate had risen

to 12 percent. At what price would the bonds sell? c. Suppose that the conditions in part a existed-that is, interest rates fell to 6

percent 2 years after the issue date. Suppose further that the interest rate remained at 6 percent for the next g years. What would happen to the price of the Ford Motor Company bonds over time?

A bond trader purchased each of the following bonds at a yield to maturity of 8 percent. Immediately after she purchased the bonds, interest rates fell to 7 percent. What is the percentage change in the price of each bond after the decline in inter­est rates? Fill in the following table:

Percentage Price @ 8% Price @ 7% Change

10-year, 10% annual coupon lO-year zero 5-year zero 30-year zero $100 perpetuity

5-3

RO E S

5·1 DPS Calculation

5-2 Constant Growth

Valuation

5-3 Constant Growth

Valuation

5-4 Preferred Stock

Valuation

5-5 Supernormal Growth

Valuation

5-6 Constant Growth

Rate, 9

5-7 Constant Growth

Valuation

5-8 Preferred Stock Rate of Return

5-9 Declining Growth

Stock Valuation

A bond that pays intere t forever and h~s no maturity date is a perpetual bond. [n what respect is a p -rpetual bond SImilar to .1 no-gr wth common rock. and to J

share of preferred 'it ck?

Warr Corporation just paid a dividend of 1.50 a share (i.e., 0 = 1.50l. The dividend is expected to grow 5 percent a year for dle next 3 ye rs, a IlL! then 10 perc 'ot year th reafter. ~ hat l5 the exp teo i idend per share for each of the next. year?

Thomas Brothers i. xpecred t pay a $0.50 per hare dividend at the enJ of I year (i.e., D I = O. ·0). Th di\ idend is e p'Lted ro grow at a constant r.He oi 7 percent a year. Th r quired rate f return on the :stock, r" is 15 percent. What is the value per shMe of the compan} 's stock?

Harri ( n Clothiers' tock Clift' ntly sell<; for 20 a share. The stock just paid a div· idend of $1.00 a ~hare (i.e., Do = $1.00). 111t~ uividend is expected to grOIl'Jt a con (nne rate of 10 percent a year. What stu k price is expected I yea r from now! What is the required rate of return on the con )30y' stock?

Fee Founders has preferred stock out tanding which pays a dividend of $5 Jt the end of each year. The pref rred stock s lis ~ Ir $60 a share. What i the prefcrre stock's required rate of return?

A company currently pays a divide d of $2 r share, Do = 2. It is e. rim3teJ thar the company's di idend will grow at a rate f 20 percent per year for rh next_ years, then the di idend will gr )'V at a can an rat of 7 percent thereaf cr. The company's stock has a beta equal to 1.2, he risk-free rate is 7.5 percent, and the market risk premium is 4 perc n . What w ul yOll estimate is the srock's currem price?

A stock is trading at $80 per share. The stoc . is e. 'pected to have a year- nd divi· dend of $4 per share (D I = 4), which is expected to grow at some con ·tant rate g throughout time. The stock's required rate of retu is 14 per nr. If you are an analyst who believes in efficient markets, what is your forecast f g?

You are considering an investment in the c mmoo srock of Keller .01')). The stock is expected to pay a dividend of $2 a share at the end of the year (D I = $2.00), The srock has a beta equal to 0.9. The ri k-frec rate is 5.6 percent and the market risk premium is 6 percent. The tock's dividend is l'xpected to grow nt sOllle can· stant rate g. The lock curren y dis for 25 a sh reo Assuming rhe l1larkt:t is in equilibrium, what does th market believe wi I be the stock price at the end of 3 years? (That is, what is P,?)

What will be the nominal rate f return on a pr ferred stock with a $100 par value, a stated dividend of 8 p rcent of par, and a current mark t price of (al 60, (b) $80, (c) $lOO, and (d) $140?

Mancil Mining Company's ore r serves are being depleted, so it all' arc tallino, Also, its pit is getting deeper ea h year, so its cost. arc rising. A a re ult, rh -.:om· pany's earnings and dividends:1r declinin at the constant rat of percent per year. If Do = $5 and r = 15%, what is t e value of Martell Mining' tock)s

182 Part 1 Fundamental Concepts

S·10 'n h ra .() Hi 'ienr tor Stock C is be ""=' 0.4, wher'3 Lbat for Stock D is bn = -0.· (St) k D's heta is negative, indicating that its rate of r'turn ri e w encver return n most ot!ll"r stocks fall. Therc are very few n any h ta tock', although l:ollection agency stocks are sometimes cited as an . mple.) a. I tht: ri k-free rate is 9 percent and the expected rat <f ret Tn ( n an aver­

age stock is 13 percent, what are the required rates of retur (11 Stocks C and ?

h. For Stol.k " suppose the current price, Po' is $25: tbe ne. t e peered dividend, D" i' '1.5 ; and the stock's expected constant gr wth rate IS 4 percent. 1 th tOl.:k in equilibrium? Explain, and describe what will app'n If the st< ck i n t

in t' uilibrtum.

A, sLIme that the average firm in your company's industry IS pe<.:ted to gr w ar a con 'tam rate of 6 p'rcent and its dividend yield is 7 percent. Your ompany i ,til Ut a risky as the average firm in the industry, but it has ju 't UCLe fuJly com­pi 'ted me R&D work that leads you to expcct that Its eamm . and dividends wiU r)W::lt a rate of 50 percent [D, = Do(I + g) = DoCI. 0)1 thl car and 2S percent the following year, after which growth should m t h th 6 percent IOdus­try average rate. The last dividend paid (D,,) was $1. What is the value per share () your firm', stock.

J ti rorech Corporation is expanding rapidly, and it curr tI needs to retain all of its carnm s; hence it does not pay any dividends. Howev r, lrtvestors expel:t MI rutech to eolO paying dividends, with the first dividend of $1.00 ollung 3 . a ~ from 0<' ay. The dividend should grow rapidly-at a ratc of 50 percent per

y ar-durin Years 4 and 5. After Year 5, the company s oui grow t c nstant rare of 8 cr nt per year. If the required rerurn on the sto k I 1 - per ent, what i' rhe value f restock roday?

5·13 Eu.dl C r or' tion issued preferred stock with a stated divlden of 1 pen.:enr of rred Stock par. Pr ferred stock of this type currently yields 8 percent, and the par alue is Valuation 100. A u e dividends are paid annually.

a. What IS t e value of Ezzell's preferred stock? b. uppo 'c interest rate levels rise to the point where the preferred rock now

yield 11 percent. What would be the value of Ezzell's prefc rred sto k?

5·14 Y ur broktr offers to sell you some shares of Bahnsen & >. l. mmon st c' that rant Growth aid dividend of $2 yesterday. You expect the divide d to r W clt he ratc of 5

IO( Valuation per e t per y ar for the next 3 years, and, if you buy the st ck, Oll plan to hold ir for ) years and then sell it. a. Find the expected dividend for each of the next 3 yf'ars' that iS l calculate Dr

D)" a cl D1. Note that Do = $2. b. Given thiu the appropriatc discount rate is 12 percent and that rhe fir't of these

diVidend p yments will occur 1 year from now, find th res nt v IUl of rhe dividend tream; that is, calculate the PY of DIt D2, and j, and then sum theloe PY.

c. You expect the price of the stock 3 years from now to b $34.73' that i you 'p Pj t equal $34.73. Discounted at a 12 perce t rate, what is the present

\·alue of thi expected future srock price? In other words, cal'ulat the PY f 4.73.

J. If you plan to buy the srock, hold it for 3 years, and then 'eli 'r for 34.73, what is th 111 sr you should pay for it?

Chapter 5 Basic Slock Valuation 183

5-15 Return on

Common Stock

5·16 Constam Growth

Stock Valuation

5·17 Supernormal Gro th

Stock Valuation

5-18 Supernormal Gr wth

Stock Valuation

e. Use Equation 5-2 to calculate the present value of thi ~rock. me that g =:

5%, and it is co tanto f. Is the value of thi' tock dependent upon bow long you plan to hold it? In

mher words, if your planned holding period w re 2 years or 5 yea. rather than 3 y ars, would this affect the value of the sto k toda, o?

You buy a share of The Ludwig C rporation toc for 2J .40. You expect it ro pay dividends of $1.07, $1.1449, and $1.22 - in ear 1 2, and 3, respectively, and you expect to sell it at a price of $26.22 at he enJ of 3 years. a. Calculate the growth rate in dividends. b. alculate the expected dividend yield. c. Assuming hat the calculated growth rate is -'1' ted to ontinu, yOll can a d

th dividend yield to the expected growth rate to get th expe red total rate of return. What is t1llS stock's expected total rate of return?

Investors require a 15 percent rate of return on Levine Com any" stock (r, =:

15%). a. What will be Levine's stock value if the prevlOus divid nd wa Do = $2 and

if investors expect dividend. to grow at a constant compound annual rate of (1) -5 per ent, (2) 0 percent, (3) 5 percent and (4) 10 perceor?

b. Using data from part a, what is the Gar on (cons, t growth) model value for Levine's stock if the required rate of return is 15 p rcent and the expecr d growth rate is (1) 15 percent or (2) 20 per 'en ? Arc e c rea onable resulrsf Explain.

c. Is it reasonable to expect that a constant growt stock would have g > r)

Wayne-Martin Electric Inc. (WME) has just devel p J a olar panel capable of gen raring 200 percent more electricity than any br panel <.:urrently on the mar­ket. s a re lilt, WME is expected to experience a 15 percent anoual growth rate fur the next 5 years. By the od of 5 years, other firms will h ve developed com­parable rechnology, and WME s growth rate wiI slow to 5 percent per year inde.f­init Iy. Stockholders require a return of 12 percent on WME's stock. The most recent annual dividend (Do), which was paid yt, terda)', as $1.75 per share. a. Calculate WME's expected dividends for t = 1, t = 2, t = 3, t = 4, and t = 5, b. Calculate the value of the stock today, PrJ' Pr 'eed by finding th present value

of the dividends expected at t = 1, t = 2, t = 3, t = 4, an~ t = 5 plus the pres­ent value of the stock price which should eXlsr at t = ,l)~. The P, stock pric can be found by using the constant growth quation. mice that to find I\, you LIse rhe dividend expected at t = 6, which is 5 percent greater than the r = 5 dividend.

c. C I ulate the expected dividend yield, O/Po, the G,lpiral gam yield expected dUring the first year, and the expected total tllrn (dividen yield plus capital

ain yield) during the first yea 1". (AsslIme th'at i~, = Po, and recognize that the capiral gains yield is equal to the total return minus the d..ividend yield.) Also calculate these same three yields for t = 5 (e.g., O/P,).

Ta J • ig Technologies Corporation (TIC) has I een gr< ~ing at a rate of 20 percent per year in recent years. This same growth rare IS exper.:te a In t for another 2 year . a. If Dll = $1.60, f, = 10%, and gil = 6%, what is IT ~'s stock worth toda !

What are its expected dividend yield and capital gain vleld at this time?

184 Part 1 Fundamen <II Concepts

• A stock's beta coefficient, b, is a measure of its market risk. Beta measurc!; the extent to whid1 the srock's returns mo\'e rel<1tivc to the market.

• A high-beta stock is more volatile than an average stock, while a low-beta stock is less volatile than an average stock. An averag~ srock has b = 1.0. The beta of a portfolio is a weighted average of the hetas of the indIvidual ecurities in the portfolio.

• n1e Security Market Line (SML) equation shows the relationship betw'een a ecurity\; rn<lrket risk and its required ratl' of rerum. The rerum rcquired for

any security i is equal to the risk-free rate plus the market risk premium tim the security's heta: rj = + (RPj\.j)b i .rRF

• Even though the expected rale of rerurn OIl a stock is generally equal to its required rerurn, a number of things can happen to cause the required [,He of rerum to change: ( I ) the risk-free rate can change hecause of change:, in either real rates or anticipated intlation, (2) a stOck's beta can change, nnd (3) investors' aversion to risk can change.

• Because returns on assets in different countries are not perfectly correlated, 'lobal diversification may result in lower risk for multinational companies a lobally diversified portfolios.

Dehne the following terms, using graphs or equations to illustrate your answers wherever feasihle: a. Stand-alone risk; risk; probability distribution h. Expected rate uf return, r c. Continuous prohahility Jistribution d. Standard deviation, (1; variance, 0'2; coefficient of variation, CV e. Risk aversion; realized rate of return, r f. Risk premium for Stock i, RI\ market risk premium, RPM g. Capital Asset Pricing Model (CAPM) h. Expected return on a portfolio, rp; market portfolio i. Correlation coefficient, p; correlation j. 'v1arket risk; diversifiabJe risk; relevant risk k. Beta coefficient, b; average srock's beta, b}\ 1. Security Market Line (SJ\!lL); SNIL equation Ill. Slope of SML as J measure of risk aversion

The probability distribution of a less risky return is morc peaked than that of a riskier return. What shape would the probability distribution have for (a) com­pletely certain returns Jnd (b) completely uncertain returns?

Security A has an expected return of 7 percent, a standard deviation of returns of 35 percent, a correlation coefficient with the market of -0.3, and a heta coeffi­cient of - 1.5. Security B has an expected rerum of 12 percent, a stanJard devia­tion of returns of 10 percent, J correlation with the market of 0.7, and a beta oefficienr of 1.0. Which security is riskier? Why?

Suppose you owned a portfolio consisting of $250,000 worth of lune-term U.S. government bonds. a. Would your portfolio be riskless? b. Now suppose you hold a portfolio conslstll1g of $250,000 worth of 30-day

Treasury bills. Every 30 days your bills mature, and you reinvest the prinCipal ($250,000) in a new batch of bills. Assume that you live on the investment

Chapter 2 Risk and Return: Part I 65

I,

1"\ l'<lLh

J "hil1nl

11~<l'I1I'd

',1 !

d,-.­

L,\\. t lit,

t: COIl1­I ' ,

lllgh~~.r

h\'l'f

II:, \:, () I

I rio,\-:

lTnl h 11­

QUESTIONS

2·1

2-2

2-3

2-4

Co

ineo e from your portfolio and that you want () maint3111 a COl ~t;).nt standard of living. Is your portfolio truly riskless? Call you think of any asset that would be completely risk css? Could someone develop such an asseU Explain.

2·5 If inve. tors' aversion to risk increased, would the risk prcl1llllm on stock increase more or less than that on a low-beta stock? 1:., plain.

a high-beta

2-6 If a company's beta w re to double, would its e 'p'cted return double?

2-7 Is it possible to co truct a portfolio of stocks which has a to the risk-free rate?

e. pe ted return equal

PROBLEMS

2-1 Expected Return

Probability of This Demand Occurring

Demand for the Company's Products

A sto k's return has the following distribution:

Rate of Return if This Demand Occurs

Weak 0.1 (50%)

Below average '0.2 (5)

Average 0.4 16 Above average 0,2 25 Strong Q.J 60

1,0

Calculate the srock' e peeted return, standard deviation, and co fficient of variation.

2-2 An individual h s 35,000 invested in a SUK whlch h· s a beta of 0.8 and Portfolio Beta $40,000 invested i a srock with a beta of 1.4. If these. re the only two invest­

ments in her porrfolio, what is her portfolio's b {a?

2·3 Assume that the ri k-free rate is S percent and the mar et ri k premi 1m is 6 percent. Expected and Required What is the expe d return for the overall -t ck marker? Whar is the required

Rates of Return rate f return on a stock that has a beta of 1.2?

2-4 A, su 1e that the ri k-free rate is 6 percent 3nd the e peeted ret 1m on the market Required Rate of Return is 13 percent. What is the required rate of return on a st ck th- t h ~ a beu of O. :

2·5 The arket and Stock J have the following prob3bility di rrib I{inns: Expected Returns

Probability

03 15% 20% 0.4 9 5 0.3 18 12

a. Calculate the e ected rates of return for tbe market and Srock J. b. Calculate the standard deviations for the m rket· nd St k J-c. Calculate the coefficients of v3riation for the marker and Stock].

2·6 ,'up ose r RF = 5%, r\,1 = 10%, and r" = 11%. Required Rate of Return a. ,alculate Stock A's heta.

b. If Stock A's hern were 2.0, WI13t ""ould he A's ne 'required rate of return?

P

R

66 Part 1 Fundamental Concepts

2·8 Portfolio Beta

2-9 'i~jOlio Required Return

2·10 Portfolio Beta

2·11 ,eauned Rate of Return

2-12 alJzed Rates of Return

Suppose r"f = 9"/.), ri\1 = 14'1,< and b i = J .3. a. What is r j , tht required rate of return on Stock i? b. Now suppose rRF (J) increases to 10 percent or (2) decreases to 8 percent.

The slope of the SML remains constant. How would this affect ri\l and I) c. Now a:>:>uITIc CRI remains at 9 percpnt hut ri\1 (I) ina'cases to 16 percent or

(2) falls to 1J percent. The slope of the SlvlL does not remain const3m. How woulJ these changes affect r j ?

Suppose )OU hold a diversified portfolill consisting of;l $7.500 investment in each of 20 different common stocks. The portfolio beta is equal to J .12. Now, !)lIPpO

you have decided to sell one of the stocks in your portfolio with a hew equal to 1.0 for $7.500 and to use these procecds to huy another stol:k for your portfolio.

SSlIlne- the ncw stock's beLl. is equal to 1.75. Calcubte your portfolio's new bet;}.

Suppose yOll are the moncy mana!!;er of a $4 million investment funo. Tue fund consists of 4 stocks with the following investments and herns~

Stock Investment Beta --- ­

A $ 400,000 150 B 600,000 (0.50)

c 1,000,000 1.25

D 2,000.000 0.75 ._-_._--_ ..

If the market required rate of return is L4 pt:rcent and the risk-free rate L" 6 per­cent, what is thl' fllnd's required rate of return?

Yuu have a $2 million portfolio consisting of oil $100,000 investment in each uf 20 different stocks. The portfolio has a beta t:qu,I1 to 1.1. You are consiJeri.ug :>elling $100,000 worth of one stock \vhich has a heta eqllal to 0.9 and l1sin~ the pro­ceeds to purCh,l"C another stock which has a bera equal to 1.4. What will be the new betn oj your portfolio following this transaction?

Stock R 11:'15 a bet,' of 1.5, Stock S has a beta of 0.75, the expected r[lte of return on an average stock is 13 percent, and the risk-free rate of r('rurn is 7 percent. By how much docs the required return on the riskier stock exceed the required return on the less risky stock?

Stocks A and n have the following historical returns:

Year Stock A's Returns, fA Stock 8's Returns, rg

2002 (18.00%) (1450%)

2003 33.00 21.80 2004 15.00 30.50

2005 (0.50) (760)

2006 27.00 26.30

a. Calculare the average rate of return for each srock during the 5-year ppriod. b. Assume [hat someone held a portfolio consisting of 50 percent of Stock A and

so percent of Stock B. What would have been the realized rate of retllm Oil. the portfolio in each yea.r? What would have heen the average return on the portfo­lio dUring this period?

c. Calculate the standard deviation of returns for each stock and for the portfolio.

Chft~Ur 1 Ill~~ ~~d ~eIUI'ri. Pdf II ~7

----

d. Calculate the coefficient of variation for each :rock and for the portfolio. e. If '0 are a risk-averse investor, would you prefer to hold Stock A, Stock B, 11

th portfolio? Why?

2·13 You hay observed the following returns over time: Expected and

Required Rates of Return; Financial

Year ---'-- ­

Stock X Stock Y Market

Calculator Needed 2002 14% 13% 12% 2003 19 7

I 10 2004 -16 -5 -12 2005 3 1 1 2006 20 11 15

Assume that the risk-free rate is 6 percent and tbe arket risk premium is S perc 'Ill a. at are the betas of Stocks X and Y? b. What are the required rates of return for Sto ks X and Y? c. rh t is the required rate of return for a por folio consisting of 80 percellt i,l

t ck X and 20 percent of Stock Y? d. If Sr ck X's expected return is 22 percent, is Stock X under- or overvalued?

S READSHEET P OBlEM

2·14 Starr with the partial model in the file IFM9 Ch02 P14 Build a Model.xls trOll

Build a Model: the ThomsonNOW Web site. Bartman Industries' and Reynolds Incorporate,i' Evaiuating Risk st ck prices and dividends, along with the Market Index, ::Ire shown below. St "

and Return prices are reported for December 31 of each ~ear and dividends reflect those I I,

during the year. The market data are adjusted t include dividends.

BARTMAN INDUSTRIES REYNOLDS INCORPORATED MARKET INDEX

Year Stock Price Dividend Stod< Price Dividend Includes Divs.

2006 $17.250 $1.15 $48.750 $3.00 11,663.98 2005 14750 1.06 52.300 2.90 8,78570 2004 16.500 1.00 48750 2.75 8,679.98 As~ 2003 10750 0.95 57,250 2.50 6,43403 fin, 2002 11.375 0.90 60.000 2.25 5,602,28 ner 2001 7.625 0,85 55.750 2.00 4,705.97 COr

$]( a. Use the data given to calculate annual rerur . for Bartman, Reynolds, allt [ht Inv,

Market Index, and then calculate average returns over the S-year period. (lIlt . bee Re lember, returns are calculated by subtracting the beginning price from ri, Fur em ing price to get the capital gain or los, adding the dividend to tbe cll' , 1 1J1V,

ain or loss, and dividing the result by the eginnjng price. Assume that dl\ anc <.lends are already included in the index. \:'0, you cannot calculate the r<1t,. .' r I

r'turn for 2001 because you do not have 2000 data.) late b. Calculate the standard deviations of the returns for Bartman, Reynolds, HI1~1 [Ii

larket Index. (Hint: Use the sample stanJ rd deviation formula given i 1 It' dev chapter, which corresponds to the STDEV function in Excel.) e

c. ow calculate the coefficients of variatio for Bartman, Reynolds, an I r sop Ntarket Index. esri

68 Part 1 Fundamental Concepts

• The feasible set of portfolios represents a II portfolios that can be constructed from a given set of assets.

• An efficient portfolio is one that offers the most return for a given amount of isk, or the least risk for a given amount of return.

• The optimal portfolio for an investor is defined by the investor's highest possi­ble indifference curve that is tangent to the efficient set of portfolios.

• The Capital Asset Pricing Model (CAPM) describes the relationship hetween market risk and required rates of return.

• The Capital Market Line (CML) describes the risklreturn relationship for effi­cient portfolios, that is, for portfolios that consist of a mix of the market port­foLo and a riskless asset.

• The Security Market Line (SML) is an integral part of the CAPM, and it describes the risklreturn relationship for individual asseb. The required rate of rerum for any Stock J is equal to the risk-free rate plus the market risk pre­mium times the stock's beta coefficient: f J = rlu + (r~'1 - rlu )bJ.

• Stock],s beta coefficient, b l , is a measure of the stock's market risk. l$eta meas­ures the volatility of retur'ns on a security relative to returns on me market, which is the portfolio of all risky assets.

• The beta coefficient is measured by the slope of the stock's characteristic line, hich is found by regressing historical returns on the srock versus histOrical

returns on the market, • Although the CAP,M provides a convenient framework for thinking abour risk

and return issues, it cannot be proven empirically, and its parameters are very difficult to estimate. Thus, the required rate of return for a stock as estimated bv the CAPM may not be exactly equa I to the true reqUIred rate of return.

• Deficiencies in the CAPM have motivated theorists to seek other risklreturn equilibrium models, and the Arbitrage Pricing Theory (APT) i~ one important new model.

• The Fama-French three-factor model has one factor for the market return, a econd factor for the size effect, and a third factor for the book-to-market

effect. • Behavioral finance assumes that investors don't always behave rationaJly.

In the next two chapters, we will see how a security's required rate of return affects its value.

QUESTION

3-1 Define the following terms, using graphs or equations to illustrate your answers wherever feasible: a. Portfolio; feasible set; efficient portfolio; efficient frontier b. Indifference curve; optimal portfolio c. Capital Asset Pricing Model (CAPM); Capital Market Line (CML) d. Characteristic line; beta coefficient, b e. Arbitrage Pricing Theory (APT); Fama-French three-factor model; behavioral

finance

3-2 ~ecurity A has an expected rate of return of 6 percent, a standard deviation of returns of 30 percent, a correlation coefficient with the marker of -0.25, and a beta coefficient of -0.5. Security B has an expected return of 11 percent., a stan­dard deviation of returns of 10 percent, a corr<:'!ation with the market of 0.75, and a beta coefficient of 0.5. Which security is illore risky? Why?

Chapter 3 Risk and R~tdrn: Part II 107

to deter-

Ie NYSE for both

d true In

ture will , it plms

!;; adding he same <and Y k should

a. Construct a scatter diagram showing the relationship between returns on Stock Y and the market. Use a spreadsheet or a calculator with a linear regression function to estimate beta.

b. Give a verbal interpretation of what the regression line and the beta coefficient show about Stock Y's volatility and relative riskiness as compared with those of other stocks.

c. Suppose the scatter of points had been more spread out, but the regression line was exactly where your present graph shows it. How would this affect (1) the firm's risk if the stock is held in a one-asset portfolio and (2) the actual risk premium on the stock if the CAPM holds exactly?

d. Suppose the regression line had been downward sloping and the beta coefficient had been negative. What would this imply about (1) Stock Y's relative riskiness, (2) its correlation with the market, and (3) its probable risk premium?

3-3 The beta coefficient of an asset can be expressed as a function of the asset's corre­Siv1L and CML lation with the market as follows:

Comparison

b; _ PiMa;

aM

a. Substitute this expression for beta into the Security Market Line (SML), Equa­tion 3-9. This results in an alternative form of the SML.

b. Compare your answer to part a with the Capital Market Line (CML), Equation 3-6. What similarities are observed? What conclusions can be dra\vn?

3-4 Suppose you are given the following information. The beta of company i, b j , is 1.1, CAPM and the the risk-free rate, rR1 ·, is 7 percent, and the expected market premium, r~1 - 1"IU, is

Fama-French 6.5 percent. (Assume that a j = 0.0.) Three-Factor Model a. Use the Security Market Line (SML) of CAPM to find the required return for

this company. b. Because your company is smaller than average and more successful than aver­

age (that is, it has a low book-to-market ratio), you think the Fama-French three-factor model might be more appropriate than the CAPM. You estimate the additional coefficients from the Fama-French three-factor model: The coeffi­cient for the size effect, c j , is 0.7, and the coefficient for the book-tn-market effect, d j , is -0.3. If the expected value of the size factor is 5 percent and the expected value of the book-to-market factor is 4 percent, what is the required return using the Fama-French three-factor model?

CYBERPROBLEM Please go to the ThomsonNOW Web site to access any Cyberproblems.

THOMSON ONE PROBLEM Please go to the ThomsonNOW Web site to access any Thomson ONE-Business School Edition problems.

Chapter 3 Risk and Return Part II 109